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A rectangular floor that is 10 feet wide and 17 feet long is tiled with 170 one-foot square tiles. A bug walks from one corner to the opposite corner in a straight line. Including the first and the last tile, how many tiles does the bug visit?

 Feb 9, 2019
 #1
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Use Pythagoras's Theorem:

 

Bug's Path^2 =10^2 + 17^2

                      =100 + 289

                      =389

                      =sqrt(389)

                      =19.72 - or ~20 tiles that the Bug crosses.

 Feb 9, 2019
 #2
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Thank you, but the answer is one of the following: 25,26,27,28

youchunhui  Feb 9, 2019
 #3
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The following diagram should help:

 

Note that the equation of the diagonal line is \(y=\frac{10}{17}x\)  As x goes in integer steps from 0 to 17, y only takes integer values at x=0 and x=17.

 Feb 9, 2019
edited by Alan  Feb 9, 2019

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